I will start by saying that the "phantom" 267M reading with the terminals open has been solved. Let me just enumerate all that was done that both did nothing to contribute to the solution, and what did.
Last night I took a whole bunch of readings around all the input elements writing down all the findings, and read the detailed theory of operation (several times) to try and get a bit more understanding on how the inputs are being processed, and perhaps finding a voltage that is off, or something missing. I even removed the rear inputs completely and even the AC board and put it aside. Needless to say the problem was still there. BTW there was a false positive at some point, in that while measuring the voltage at pin 18 of U101 (same node as U213 pin 3) I saw in the corner of my eye GOHM on the display on the 300M range. But this was short lived, as it turns out with open inputs the indication was rather 0.0000 GOHM, and not the correct OVLD GOHM. But at least got to see the "GOHM" text on the display, so that was at least a bit uplifting. I also noticed that this would even happen with the black return lead of the external DMM disconnected and only the red lead at pin 18. So I assume some noise was being introduced that was somehow masking whatever was causing the 267M phantom reading.
Anyway, I could not find anything wrong with any of the measurements other than some of them did not seem right specially for the 30/300M ranges but they where clearly being affected by the portable external DMM I was using (the 974A) that "only" has a 10M input Z. So next tried using the 3.0V range of the 3478A (BTW I also have a 3468A) which has 10^10 ohms input Z and it worked better in a couple of spots but in others it would just cycle about every second between reading the voltage (about 1.1V) and then showing overload as I had it in manual range so it would actually stay in the 3V range I then tried also with the 3468A but got exactly the same result. I was puzzled by this because the portable DMM showed there was just 1.1V at the node with a perfectly stable reading (only loaded down by its lower internal Z), no pulses no variations. I even put a scope on the node and of course there was nothing but DC there. So I assume some kind of common mode current was creeping between the measurement point in the 3457A and the 3468/3478. I did check the ripple on all 3 DC busses +15, -15, and +5 and all looked very clean.
While trying to understand further some of the elements I started measuring voltages around U214 the Harris analog switches. Something did not seem right as in the schematic the terminal of pins 3 and 4 had very different voltages (15v and 4V) and yet that switch is shown as closed in the schematic, and voltages where equal between switch pins 1 and 16 (both 4V), even tough that switch is shown as open in the schematic. And furthermore the 5V steering logic of the switches seemed to be stuck on Hi all the time. I did not have any external resistor connected to the input terminals so later found out that when in OVLD condition the steering logic only start switching states when there is actually some resistance connected to the input to be measured. Also found the datasheet of the Harris HI3-0390-5 chip, and was able to understand how it works and everything fell in place and it was just that the schematic is actually showing the switches in the opposite position to being in the 2W OVLD condition which is what I had at the time. Long story short, there was nothing wrong the IC214. But at least I was able to fully understand its operation and function. Also among others also understood how the ohms current source works by using the 4 current setting resistors inside U101, and about the voltage difference of 4V (12V-8V) to generate the test current for all but the 30/300M ranges, for which only 0.4V (8.4V-8V) are used instead.
I basically went on like this with the other areas of the input signal conditioning section and determined by reading the output voltage going to the ADC while connecting some external resistors to the input and measuring the resulting voltages it showed that all ranges except the 300M where behaving correctly, and only the 300M input to the ADC seemed wrong, so at the very least I knew the problem was definitively upstream from the ADC. Anyway, it was then close to 3am so went to bed and let the ideas churn around a bit and start fresh in the morning.
So next morning one of the first things that popped into my mind is what if the 300M range problem showing 267M with no input is just related to the unit being uncalibrated. Why not attempt a Volt and 2/4W calibration with values as close as possible just to get through the procedure notwithstanding any inaccuracies which at this point would not really be that important.
Started by doing all the preliminary calibration procedures: run a self test, which resulted in a hardware error, which of course was due to the AC board being on the other end of the table. I then connected it back and the self-test went OK this time. Now on to running an Autocal routine which also went without any issues.
So let me just quickly check again the 300M range, nope, still have the same problem, its not going to be that easy. So on with the next calibration procedures: DC Offset cal. I do have two heavy #6 solid copper wire U shaped jumpers that are ideal. All ranges starting with 300V and down calibrated fine to zero.
Now volts gain calibration. For this step I used a hi-volt capacitor restorer that outputs 150-600V, and trimmed it as close as possible for 300V with a variac and calibrated the 300V range. Then used my variable power supply for the 30V range, the MAX chip voltage standard I build for the 3V range, and then used a 5K 10T potentiometer fed from the 3V standard to dial in 300mV and 30mV to cal those two remaining ranges. All went well, no issues at all. Then did the 3V linearity calibration by reversing the polarity as indicated in the manual, and that too went well.
Maybe 300M range working now? No.
Next calibrate 2W ohms. For this I used pairs of soldered together 1/4w 5% resistors (3x 10M for the 30M "standard") just to get into the ballpark of full scale for all the ranges, and checked them with the 974A and wrote down the average values. Most where slightly under like 2.969M, 295.150K, 29.839K, 2.9675K, 297.55R, and 29.66R. Only the 30M string was slightly above FS, at 30.050M. I started calibrating all ranges starting with the 30M and down, and all went well.
Time to check again on that 300M range indication, and YES, it now showing "OVLD GOHM" with nothing attached to the inputs. Success!
Anyway I though while I'm here, let me also do the 4W ohms offset and gain calibrations as well. I do have two of those heavy copper U shaped jumpers, and both where connected together with another short piece of wire and all ranges starting with 300M and down where successfully set to zero. Then did the gain calibration of all ranges, again starting from the top 300M and down, and again all good.
Looked again at the 300M 2W indication, and yes, its still good indicating OVLD GOHM.
So guess at this point I have a "fake" calibration of the volts and 2/4W ranges, and that definitively solved the problem, which really was never a problem, just lack of calibration. Hope this helps someone in the future encountering a similar situation. Time to button up the 3457A, and start thinking how to get it properly calibrated. Unfortunately where I live there are no calibration facilities, none. I am outside of the US, and my "closest" facility would probably be in Miami FL, or perhaps Puerto Rico, but I am guessing that Fedexing this instrument would cost about the same to either destination and I feel more confident about mainland USA for a decent calibration which I still don't even know how much it is going to cost. My other alternative would be to get a calibrator to me, but I am not prepared to spend hundreds (or thousands) of $$$ on something that matches the calibration accuracy requirements of this DMM. I really only would need hobby level accuracy, so i was thinking that another possibility would be to build a DC calibrator that would at least include 30 and 300mV, 3V and perhaps also 30V, which I anticipate would be the ranges I would use most. And then get from Mouser or Digikey a set of resistors with best possible accuracy and values to calibrate the 2/4W ohms ranges. And then send both the voltage "standards" and resistors off to someone with a 3458 or Fluke 732 to just characterize the values for me with documented environmental conditions so I could hopefully replicate them as closely as possible, and then send them back to me. I would of course be happy to pay for all shipping and cover time involved up to a reasonable amount. In general I am happy with my 3468A and 3478A performing quite adequately, but once you get to the level of a 3457A, well it would really be an injustice to just get it ball parked, it really deserves the best possible and viable calibration given the logistical limitations. I wish the backup battery had not died who knows when and calibration was lost, as intact calibration constants from the last good calibration procedure would have probably been enough for me, at least for a while.
Sorry for the long post, but I had a quite bit I wanted to document, so thanks for reading if you made it this far.
EDIT: added 2x pictures.
EDIT2: couple of spelling corrections